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SPECIFICATION TESTS FOR LATTICE PROCESSES

Published online by Cambridge University Press:  19 August 2014

Javier Hidalgo  and
Myung Hwan Seo
Javier Hidalgo
Affiliation:
London School of Economics and Seoul National University
Myung Hwan Seo*
Affiliation:
London School of Economics and Seoul National University
*
*Address correspondence to Myung Hwan Seo, London School of Economics, Houghton St., London WC2A 2AE, UK; e-mail: m.seo@lse.ac.uk.; or to: Seoul National University, Kwan-Ak Gu, Seoul, Korea.
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Abstract

We consider an omnibus test for the correct specification of the dynamics of a sequence $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One first main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analog of the transformation and show its validity. Thirdly, we discuss the results when $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimator of the parameters of the regression model under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the finite sample behavior of our test.

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ARTICLES
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Econometric Theory , Volume 31 , Issue 2: Haavelmo Memorial Issue: Part Two , April 2015 , pp. 294 - 336
Copyright
Copyright © Cambridge University Press 2014 

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